Existence and uniqueness for the transport of currents by Lipschitz vector fields

DOI10.1016/j.jfa.2024.110315arXiv2303.03218MaRDI QIDQ6119943

Giacomo Del Nin, Filip Rindler, Paolo Bonicatto

Publication date: 20 February 2024

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2303.03218

zbMATH Keywords

currentscontinuity equationLie derivativedecomposibility bundle

Mathematics Subject Classification ID

Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Continuity and differentiation questions (26B05) Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives (26A27) Transport equations (35Q49)

Cites Work

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• Well-posedness for the continuity equation for vector fields with suitable modulus of continuity
• Non-uniqueness of signed measure-valued solutions to the continuity equation in presence of a unique flow
• Space-time integral currents of bounded variation
• Elasto-plastic evolution of single crystals driven by dislocation flow

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